How interfaces work and how they are used. Clarification help.

I understand that interfaces create methods that can be used in other classes, but it is up to the class that uses it to tell it how the interface's method actually works. So, I think that, when something "implements" an interface, it simply says that this new class uses the method names of the interface and possibly the same arguments. I can't figure out why you would implement an interface like the video does by overriding the compareTo() method instead of just creating a fully implemented method, unless it is simply to prevent runtime errors if for some reason another class tries to use the objects method, in this case the Treet.compareTo() method, to compare it to something that is not a Treet. Is this the use for interfaces and implementation to prevent inadvertent runtime errors and instead catch them when compiling?